San, Damla
Reduced order models (ROM) play a crucial role in tackling the computational challenges posed by complex flow simulations. They provide an effective solution to the resource-intensive demands of direct numerical simulations. Among the techniques utilized for constructing reduced-order models, proper orthogonal decomposition (POD) stands out as a frequently employed method with applications spanning diverse fields of engineering and science. Despite its initial appeal as a means to attain both computational efficiency and precise representation of coherent structures in turbulent flows at high Reynolds numbers, the full realization of this potential remains a goal to be achieved. Appropriate closure modeling methodologies should be used to achieve an ideal combination between the lowest computing cost inherent in ROM and the complexities of the targeted flows. This thesis employs a combination of innovative physics-based and data-driven modeling tools to develop more robust and improved frameworks for ROM in complex flows. In this thesis, the core concepts of the ROM are introduced, centered around utilizing reduced bases generated from snapshots. Applying techniques like POD and Galerkin Projection is demonstrated through numerical results involving diverse flow equations, ranging from the Burgers equation to the Navier-Stokes equations. The primary focus is on addressing the challenges arising from the dynamic changes inherent in turbulent flows, which can limit conventional ROM methods. To enhance the accuracy of the ROM approximation, a closure term is formulated using machine learning methods. Each chapter begins by outlining the full-order model (FOM) employed to generate snapshots representing the flow across different instantaneous time points for each equation. Subsequently, the steps taken in reduced-order modeling are detailed. By comparing outcomes obtained from the full-order model to those derived using POD and Galerkin Projection, an assessment is made to demonstrate the accuracy and efficiency of these methods in reducing computational complexity and providing accurate solutions for complex fluid flow problems.
Citation Formats
D. San, “DATA-DRIVEN REDUCED-ORDER MODELING FOR COMPUTATIONAL FLUID DYNAMICS,” M.S. - Master of Science, Middle East Technical University, 2023.